Bridging Statistical Scattering and Aberration Theory: Ray Deflection Function -- II: Numerical Validation

TL;DR

This paper experimentally validates a new Ray Deflection Function approach that unifies statistical scattering and aberration theories in optical surface roughness modeling, confirmed through detailed ray tracing simulations.

Contribution

It introduces and validates a novel RDF-based method that bridges statistical scattering models and deterministic aberration analysis in optical systems.

Findings

RDF method accurately models surface roughness effects.

Statistical equivalence between HS and RDF-based approaches.

Close agreement in near-focal-plane distributions.

Abstract

This paper presents a comprehensive experimental validation of a recently developed Ray Deflection Function (RDF) approach, which offers a new framework for modeling surface roughness effects in optical systems. Through detailed geometrical ray tracing simulations, we demonstrate that the RDF methodology successfully bridges two traditionally separate domains: statistical scattering models and deterministic aberration analysis. We implement and compare the two approaches for modeling a parabolic mirror with surface imperfections with three cases: (1) an ideal parabolic mirror baseline, (2) the conventional Harvey-Shack (HS) statistical scattering theory applied to ray perturbations, and (3) the newly proposed aberration term method based on the RDF theory. Our results confirm the statistical equivalence between the HS approach and the RDF-based aberration term method, with both producing close near-focal-plane distributions and focal volume characteristics. By establishing this equivalence, we validate that surface roughness effects can be accurately represented as deterministic aberration terms while maintaining fidelity to established statistical scattering models.